Quote of the Day

Son, this is a Washington, D.C. kind of lie. It's when the other person knows you're lying, and also knows you know he knows.

## Introduction

I needed to estimate the loss on a fiber network today – something that I have done hundreds of times before. However, today was a bit different because I decided to look at how sensitive my results were to my assumptions on when the fiber was deployed. I was a bit surprised to see how much fiber has improved with respect to losses due to contamination by OH molecules, a problem often referred to as the water peak.

This post graphs fiber loss data (Figure 1) based on:

- Corning SMF-28e fiber specification, a modern G.652-compliant fiber. This fiber has been around since the early 2000's.
- empirical data from 1990 fiber deployments using G.652-compliant fiber
- empirical data from 2000 fiber using G.652-compliant fiber
- empirical data from 2003 fiber using G.652-compliant fiber
- a common equation-based model.

I thought the results were interesting and worth sharing here (Figure 1).

## Background

### Definitions

- attenuation (aka loss)
- Attenuation in fiber optics, also known as transmission loss, is the reduction in intensity of the light beam (or signal) with respect to distance traveled through a transmission medium. (Source)
- attenuation coefficient
- Optical power propagating in a fiber decreases exponentially with distance by the formula , where
*P(z)*is the optical power at distance*z*,*P*is the launch power, and_{0}*α*is the attenuation coefficient. We normally express the attenuation coefficient in terms of dB/km, which allows us to compute system losses using simple addition. - water peak
- A peak in attenuation in optical fibers caused by contamination from hydroxyl (OH) ions that are residuals of the manufacturing process. Water peak causes wavelength attenuation and pulse dispersion in the region of 1383 nm. (Source)

### Loss Modeling

Fiber optics losses are modeled by assuming a fraction of the light power is lost through each component. These losses are expressed in terms of dB. For example:

- fusion splices: ~0.07 dB
- mechanical splices: 0.4 dB
- splitters: ~16 dB (32-way split)
- fiber: 0.25 dB/km for 1550 nm.

When expressed in dB, the losses can be added to provide a total loss. For more modeling information and an example, see this page.

## Analysis

### Corning Loss Model

I normally use the Corning loss model because virtually all my customers use Corning SMF-28e fiber. To assist customers with estimating fiber loss per km, Corning provides a spreadsheet (it contains a macro) with a simple model that uses the loss at a long wavelength, short wavelength, and at the water peak. For normal work, I use the values shown in Figure 2, which is from the SMF-28e specification sheet.

I should mention that the raw fiber attenuation is slightly lower than the loss after it is been put into a cable. This is because the act of cabling tends to add microstresses (also known as microbends) to the fiber that increase its attenuation. At my company, we assume that the cabling penalty is ~0.05 dB/km.

### ITU-T G.652 Compliant Cable

The ITU has published a standard for optical fiber called ITU-T G.652. They have supplemented this standard with a document that contains measured data for cabled fiber. This data is interesting because it provides information I have never seen elsewhere:

- fiber loss per km plus the standard deviation of the loss (i.e. variation across fiber segments). I often need to estimate the "worst-case" fiber loss and the standard deviation allows me to use the RSS method.
- fiber loss per km for fiber installed during different years (1990, 2000, 2003). The fiber loss per km is different between the three years, particularly at the water peak. This data shows that fiber is greatly improved with respect to the water peak.

I should mention that G.652 sets the minimum standard for fiber. Manufacturers often compete by having a better attenuation coefficient, ability to handle more power before the onset of nonlinearities (e.g. SMF-28e+), zero water peak, or supporting a tighter bend radius (e.g. bend insensitive fiber).

### Equation-Based Loss Model

I occasionally see people model fiber loss (example) using Equation 1, which ignores the water peak . Equation 1 assumes that the attenuation versus wavelength is entirely due to Rayleigh scattering, which is accurate if you ignore the water peak.

Eq. 1 |

where

*R*is the attenuation factor at the reference wavelength λ_{λ0}_{0}.*C*is a constant that varies with the reference wavelength λ_{λ0}_{0}.*λ*is the wavelength at which I want to compute the attenuation factor.*α*is the attenuation coefficient at λ.

## Conclusion

Fiber deployments generally avoid wavelengths near the water peak of 1383 nm because of the excess loss there. I thought it was interesting to see how the water peak has changed so much over the last 17 years. Note that Corning's specifications show its water peak is larger than was measured on the empirical data from the 2003 deployment. I assume this is because they measured some fiber networks with zero water peaks, which would drop the average.

The Equation 1 model works well as long as you are far from the water peak. I will be using Equation 1 for my simple modeling tasks because:

- None of my wavelengths are near the water peak.
- Equation 1 is easy to evaluate in Excel, and all of my customers have Excel.
- It is quite accurate for wavelengths far from the water peak.